Question: Multiply the following complex numbers, marked as blue dots on the graph: $[4(\cos(\frac{3}{2}\pi) + i \sin(\frac{3}{2}\pi))] \cdot [2(\cos(\frac{1}{6}\pi) + i \sin(\frac{1}{6}\pi))]$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $4(\cos(\frac{3}{2}\pi) + i \sin(\frac{3}{2}\pi))$ ) has angle $\frac{3}{2}\pi$ and radius $4$ The second number ( $2(\cos(\frac{1}{6}\pi) + i \sin(\frac{1}{6}\pi))$ ) has angle $\frac{1}{6}\pi$ and radius $2$ The radius of the result will be $4 \cdot 2$ , which is $8$ The angle of the result is $\frac{3}{2}\pi + \frac{1}{6}\pi = \frac{5}{3}\pi$ The radius of the result is $8$ and the angle of the result is $\frac{5}{3}\pi$.